Adaptive Controller Design for Unknown Systems Using Measured Data

This paper presents a measurement‐based adaptive control design approach for unknown systems working over a wide range of operating conditions. Traditional control design approaches usually require the availability of a mathematical model. However, it has been shown in many practical situations that, due to complex dynamics of physical systems, some simplifying assumptions are made for the derivation of mathematical models. Hence, controller design based on simplified models may result in degradation of the desired closed‐loop performance. Data‐based control design approaches can be viewed as an alternative approach to model‐based methods. Most data‐based control methods available in the literature aim to design controllers for unknown systems that operate only at a given operating point. However, the dynamical behavior of plants may change for different operating conditions, which makes the task of designing a controller that works over the entire range of operating conditions more challenging. In this paper, we address such a problem and propose to design adaptive controllers based on measured data. Such a proposed method is based on designing a set of measurement‐based controllers validated at a finite set of pre‐specified operating points. Then, the parameters of the adaptive controller are obtained by interpolating between the set of pre‐designed controller parameters to derive a gain‐scheduling controller. Moreover, low‐order adaptive controllers can be designed by simply selecting the desired controller structure. The efficacy of the proposed approach is experimentally validated through a practical application to control a heating system operated over a large range of flow rate.     

Passivity‐based control of a magnetically levitated flexible beam

This paper solves the asymptotic stabilization problem for a magnetically levitated flexible beam using a nested‐loop passivity‐based controller design. Passivity analyses reveal that the system can be decomposed into two passive subsystems: a mechanical subsystem that consists of a flexible beam with both ends free and that defines a passive map from external forces to the velocity of the points on the flexible beam at which the external forces act; and an electrical subsystem that consists of a pair of electromagnets and that defines a strictly output‐passive map from voltages applied across the electromagnets to magnetic fluxes. The standard method for designing passivity‐based controllers leads to a nonlinear feed‐forward controller for the electrical subsystem, which enables the electrical subsystem to generate given desired magnetic forces, and an output feedback compensator for the mechanical subsystem, which computes the desired forces required to regulate the position and vibration of the beam. The asymptotic stability of each controller may be proven using Lyapunov's stability theory and LaSalle's invariant set theorem. Numerical simulations confirm the asymptotic stability of the equilibrium configuration of the closed‐loop system formed by the magnetically levitated flexible beam together with the proposed controllers. Copyright © 2008 John Wiley & Sons, Ltd.     

ROBUST OUTPUT FEEDBACK CONTROLLER DESIGN WITH COVARIANCE AND DISC CLOSED‐LOOP POLE CONSTRAINTS

This paper is concerned with the problem of robust output feedback controller design for a class of linear discrete‐time systems with normbounded uncertainty. The objective is to design a controller such that the closed‐loop poles are assigned within a specified disc and the steady regulated output covariance is guaranteed to be less than a given upper bound. Using a linear matrix inequality (LMI) approach, the existence conditions of such controllers are derived, and a parametrized characterization of a set of desired controllers (if they exist) is presented in terms of the feasible solutions to a set of LMIs. A procedure is given to select a suitable output feedback controller that minimizes the desired control effort.     

Pid And Pid‐Like Controller Design By Pole Assignment Within D‐Stable Regions

This paper presents a new PID and PID‐like controller design method that permits the designer to control the desired dynamic performance of a closed‐loop system by first specifying a set of desired D‐stable regions in the complex plane and then running a numerical optimisation algorithm to find the controller parameters such that all the roots of the closed‐loop system are within the specified regions. This method can be used for stable and unstable plants with high order degree, for plants with time delay, for controller with more than three design parameters, and for various controller configurations. It also allows a unified treatment of the controller design for both continuous and discrete systems. Examples and comparative simulation results are provided to illustrate its merit.     

Pointwise in frequency performance weight optimization in µ‐synthesis

A conceptually different approach to the µ‐synthesis robust performance problem is proposed in this article. The optimization problem posed maximizes the performance weights with respect to a suitable cost function that captures the desired closed‐loop performance. This maximization of performance weights is limited by the fact that there must exist some internally stabilizing controller that guarantees robust performance with respect to these maximized weights. Thus, performance weights and a controller that achieves an optimized level of robust performance are synthesized together by one algorithm in a systematic way. The designer is only required to specify the plant set and an optimization directionality. This directionality only appears in the cost function and reflects the desired closed‐loop properties in particular frequency regions. It is pointed out that choosing this directionality is much easier than choosing the performance weights directly. Correspondingly, this approach greatly simplifies the often long and tedious process of designing ‘good’ performance weights directly and gives an indication of what is the achievable performance. A pointwise in frequency solution to the posed optimization problem is also developed in this article. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust model predictive control for polytopic uncertain systems with state saturation nonlinearities under Round‐Robin protocol

This paper is concerned with the robust model predictive control (RMPC) problem for polytopic uncertain systems with state saturation nonlinearities under the Round‐Robin (RR) protocol. With respect to the practical application, one of the most commonly encountered obstacles that stem from the physical limitation of system components, ie, state saturation, is adequately taken into consideration. In order to reduce the network transmission burden and improve the utilization of the network from the controller nodes to the actuator node, a so‐called RR protocol is employed to orchestrate the data transmission order. At each transmission instant, only one controller node that obtains the priority is accessible to the shared communication network. Our aim of the underlying problem is to design a set of controllers in the framework of RMPC such that the closed‐loop system is asymptotically stable. By taking the influence of the RR protocol and the state saturation precisely into account, some sufficient criteria are established in terms of the token‐dependent Lyapunov‐like approach. Then, an online optimization problem subjected to some matrix inequality constraints is provided, and the desired controllers can be obtained by solving the certain upper bound of the objective addressed. Finally, a distillation process example is provided to illustrate the effectiveness of the proposed RMPC approach.     

A feedforward–feedback controller for infinite‐dimensional systems and regulation of bounded uniformly continuous signals

We design a controller for infinite‐dimensional linear systems (with bounded control, observation and feedthrough operators) which, under certain assumptions, achieves asymptotic tracking of arbitrary bounded uniformly continuous reference signals in the presence of disturbances. The proposed controller is of feedforward–feedback type: The dynamic feedback part is used to stabilize the closed‐loop system consisting of the plant and the controller, whereas the feedforward part is tuned using the regulator equations to achieve the regulation of desired signals. We also completely solve the regulator equations for SISO systems, and we discuss robustness properties of the proposed controller. A useful feature in our design is that the feedforward part of the controller can be designed independently of the feedback part. This automatically leads to a degree of robustness in the stabilizing part of the controller, which is not present in the existing state feedback controllers solving the same output regulation problem. Copyright © 2006 John Wiley & Sons, Ltd.     

Application of the Hirsch Generic Convergence Statement to the Set‐Point Regulation of Excitable‐Transparent‐Monotone Systems

Monotone systems are dynamical systems whose solutions preserve an ordering, relative to the initial data. This paper focuses on the set‐point regulation problem for excitable‐transparent‐monotone single‐input single‐output systems with well‐defined static characteristics. The suggested technique for designing a static feedback controller is inspired from the Hirsch Theorem for monotone autonomous systems. It is shown that the closed‐loop system is strongly monotone and its generic solution converges to the desired set‐point. A remark is given on the application of the suggested design methodology to delay systems, as well as to systems with reaction‐diffusion equations. A simulation example from the biological world demonstrates the effectiveness of the proposed control strategy in real applications.     

Multirate sampled‐data stabilization for a class of low‐order lower‐triangular nonlinear systems

This paper investigates the problem of sampled‐data controller design for a class of lower‐triangular systems in the p‐normal form (0<p<1). A multirate digital feedback control scheme is proposed to achieve the global strong stabilization of the sampled‐data closed‐loop system under some assumptions. In the design of the controller, the input‐Lyapunov matching strategy and multirate control approach are combined to obtain better stabilizing performance. Unlike the design method based on the approximate discrete‐time model, our controller is obtained from the exact discrete‐time equivalent model, which does not need to be computed completely. The approximate multirate digital controllers are proved to be effective in the practical implementation. It is shown that, compared with the emulated control scheme, our controller may provide faster decrease of Lyapunov function for each subsystem. This will lead to allow large sampling periods. An illustrative example is provided to verify the effectiveness of the proposed control scheme.     

Linear Model‐based Feedforward Control for Improving Tracking‐performance of Linear Motors

The main purpose of this article is to propose a linear model‐based approach for improving the tracking performance of linear motors. In particular, P‐ and PI‐controllers, augmented with a linear‐model‐based feedforward controller and disturbance observer (DOB), were utilized in this research. Experimental results show that the feedforward controller can substantially reduce the phase‐delay problem resulting from the limitation of closed‐loop bandwidth. In addition, the DOB can reject nonlinear behaviors to keep a motor‐system close to our nominal linear model. Compared with the results of using P‐ and PI‐controllers only, tracking errors were reduced from 4.44% to 0.67% of the desired trajectory. Therefore, the proposed method provides a solution for improving the tracking performance of linear motors.     

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

This paper is concerned with the problem of H_∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H_∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H_∞ output tracking controller design.     

Reliable memory feedback design for a class of non‐linear time‐delay systems

This paper is concerned with the robust controller design of uncertain time‐delay systems with unknown nonlinearity and actuators failures. New methods for designing stabilizing controllers and reliable controllers are proposed. The stability criteria of the closed‐loop system, which are dependent on the magnitudes of the delay and its derivative, are derived in the form of linear matrix inequalities. Numerical and simulation results are provided to demonstrate the effectiveness of the proposed results, as well as the reduction of conservativeness when compared with existing ones. Copyright © 2004 John Wiley & Sons, Ltd.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

Optimal fixed‐structure control for linear non‐negative dynamical systems

In this paper, we develop optimal output feedback controllers for set‐point regulation of linear non‐negative dynamical systems. Specifically, using a constrained fixed‐structure control framework we develop optimal output feedback control laws that guarantee that the trajectories of the closed‐loop system remain in the non‐negative orthant of the state space for non‐negative initial conditions. In addition, we characterize domains of attraction predicated on closed and open Lyapunov level surfaces contained in the non‐negative orthant for unconstrained optimal linear‐quadratic output feedback controllers. Output feedback controllers for compartmental systems with non‐negative inputs are also given. Copyright © 2004 John Wiley & Sons, Ltd.     

Multiple robust H∞ controller design using the nonsmooth optimization method

This paper proposes a systematic technique to design multiple robust H_∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed‐loop performance when a single robust controller cannot achieve satisfactory performance. Copyright © 2009 John Wiley & Sons, Ltd.     

Non‐parametric linear time‐invariant extensions of non‐invertible and backlash plant

A rigorous validation for the use of a set of linear time‐invariant models as a surrogate in the design of controllers for uncertain nonlinear systems, which are invertible as one‐to‐one operators, such as used in the nonlinear quantitative feedback theory (NLQFT) design methodology has been given by Baños and Bailey. This paper presents a similar validation but weakens the requirement on the invertibility of the nonlinear plant by application of Kakutani's fixed‐point theorem and an incremental gain constraint on the plant within its operational envelope. The set of linear time‐invariant models to be used for design is shown to be an extension (termed here the linear time‐invariant extension—LTIE) of the nonlinear plant restricted to the desired output operating space. A new non‐parametric approach to the modelling of the LTIE is proposed which is based on Fourier transforms of the plant I/O data and which accordingly may be based solely on experimental testing without the need for an explicit parametric plant model. This new approach thus extends the application of robust linear controller design methods (including those of NLQFT) to nonlinear plants with set‐valued (multi‐valued) inverses such as those containing backlash and also to plants for which explicit parametric models are difficult to obtain. The method is illustrated by application of the non‐parametric approach to an NLQFT tracking controller design for a mechanical backlashed servomechanism problem. Copyright © 2013 John Wiley & Sons, Ltd.     

Finite‐time tracking control of a nonholonomic mobile robot

In this paper, the finite‐time tracking problem is investigated for a nonholonomic wheeled mobile robot in a fifth‐order dynamic model. We consider the whole tracking error system as a cascaded system. Two continuous global finite‐time stabilizing controllers are designed for a second‐order subsystem and a third‐order subsystem respectively. Then finite‐time stability results for cascaded systems are employed to prove that the closed‐loop system satisfies the finite‐time stability. Thus the closed‐loop system can track the reference trajectory in finite‐time when the desired velocities satisfy some conditions. In particular, we discuss the control gains selection for the third‐order finite‐time controller and give sufficient conditions by using Lyapunov and backstepping techniques. Simulation results demonstrate the effectiveness of our method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A measurement-based approach for designing reduced-order controllers with guaranteed bounded error

The objective of this paper is to present a measurement-based control-design approach for single-input single-output linear systems with guaranteed bounded error. A wide range of control-design approaches available in the literature are based on parametric models. These models can be obtained analytically using physical laws or via system identification using a set of measured data. However, due to the complex properties of real systems, an identified model is only an approximation of the plant based on simplifying assumptions. Thus, the controller designed based on a simplified model can seriously degrade the closed-loop performance of the system. In this paper, an alternative approach is proposed to develop fixed-order controllers based on measured data without the need for model identification. The proposed control technique is based on computing a suitable set of fixed-order controller parameters for which the closed-loop frequency response fits a desired frequency response that meets the desired closed-loop performance specifications. The control-design problem is formulated as a nonlinear programming problem using the concept of bounded error. The main advantages of our proposed approach are: (1) it guarantees that the error between the computed and the desired frequency responses is less than a small value; (2) the difficulty of finding the globally optimal solution in the error minimisation problem is avoided; (3) the controller can be designed without the use of any analytical model to avoid errors associated with the identification process; and (4) low-order controllers can be designed by selecting a fixed low-order controller structure. To experimentally validate and illustrate the efficacy of the proposed approach, proportional-integral measurement-based controllers are designed for a DC (direct current) servomotor.     

A partially delay‐dependent and disordered controller design for discrete‐time delayed systems

This paper considers the stabilization problem for a class of discrete‐time delayed systems by exploiting a partially delay‐dependent controller whose gains suffer a disordering phenomenon simultaneously. Two stochastic variables are used to describe the partially delay‐dependent and disordering properties, which are not independent, and referred to the original operation modes here. By introducing an augmented Markov chain, the corresponding closed‐loop system is transformed into a Markovian jump system with four new operation modes (NOMs). Based on the proposed model, a kind of controller depending on NOMs is firstly proposed with linear matrix inequalities forms. Moreover, without designing a controller containing NOMs directly, another kind of stabilizing controller referring to one depending on original operation modes is developed, which is composed of a series of NOM‐dependent controllers and satisfies a minimum variance approximation. Finally, two numerical examples are used to demonstrate the utility and superiority of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Fuzzy Sliding‐mode Strategy for Air–fuel Ratio Control of Lean‐burn Spark Ignition Engines

Minimization of emissions of carbon dioxide and harmful pollutants and maximization of fuel economy for lean‐burn spark ignition (SI) engines relies to a large extent on precise air–fuel ratio (AFR) control. However, the main challenge of AFR control is the large time‐varying delay in lean‐burn engines. Since the system is usually subject to external disturbances and uncertainties, a high level of robustness in AFR control design must be considered. We propose a fuzzy sliding‐mode control (FSMC) to track the desired AFR in the presence of periodic disturbances. The proposed method is model free and does not need any system characteristics. Based on the fuzzy system input–output data, two scaling factors are first employed to normalize the sliding surface and its derivative. According to the concept of the if‐then rule, an appropriate rule table for the logic system is designed. Then, based on Lyapunov stability criteria, the output scaling factor is determined such that the closed‐loop stability of the internal dynamics with uniformly ultimately bounded (UUB) performance is guaranteed. Finally, the feasibility and effectiveness of the proposed control scheme are evaluated under various operating conditions. The baseline controllers, namely, a PI controller with Smith predictor and sliding‐mode controller, are also used to compare with the proposed FSMC. It is shown that the proposed FSMC has superior regulation performance compared to the baseline controllers.